Solving illposed inverse problems using iterative deep neural networks
Abstract
We propose a partially learned approach for the solution of illposed inverse problems with not necessarily linear forward operators. The method builds on ideas from classical regularisation theory and recent advances in deep learning to perform learning while making use of prior information about the inverse problem encoded in the forward operator, noise model and a regularising functional. The method results in a gradientlike iterative scheme, where the ‘gradient’ component is learned using a convolutional network that includes the gradients of the data discrepancy and regulariser as input in each iteration.
We present results of such a partially learned gradient scheme on a nonlinear tomographic inversion problem with simulated data from both the SheepLogan phantom as well as a head CT. The outcome is compared against filtered backprojection and total variation reconstruction and the proposed method provides a 5.4 dB PSNR improvement over the total variation reconstruction while being significantly faster, giving reconstructions of 512 × 512 pixel images in about 0.4 s using a single graphics processing unit (GPU).
 Publication:

Inverse Problems
 Pub Date:
 December 2017
 DOI:
 10.1088/13616420/aa9581
 arXiv:
 arXiv:1704.04058
 Bibcode:
 2017InvPr..33l4007A
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Artificial Intelligence;
 Mathematics  Functional Analysis;
 Mathematics  Numerical Analysis
 EPrint:
 Inverse Problems 2017